Abstract
In this talk I will discuss a method of building families of graphs using certain systems of polynomial equations over commutative rings. Graphs from these families have found many applications in various parts of graph theory and beyond. We briefly survey some of the older results, and mention several new ones. A few open problems related to these families of graphs will be mentioned.
About the speaker
Professor Lazebnik received an equivalent of a Master Degree in Mathematics from Kyiv State University in 1975 under supervision of Professor L.A. Kaluzhnin and Dr. M.H. Klin. Then, for four years, he worked as a teacher of mathematics at The Ukrainian Physics and Mathematics (boarding) High School affiliated with Kyiv State University. He received his Ph. D. in Mathematics from The University of Pennsylvania in 1987 under supervision of Professor H.S. Wilf. From 1987 to 2023, he worked at the Department of Mathematical Sciences, University of Delaware, where nowadays he is an Emeritus Professor. His main research interests are in combinatorics, graph theory, algebra and geometry.
Professor Lazebnik likes teaching and working with students at all levels. Fifteen students received their Ph. D. under his supervision. For many years, he has been a member of the Editorial Board of The Electronic Journal of Combinatorics, where he served as the Managing Editor for five years.
